Illusion Game Reliability

Preprocessing

Preprocessing

library(tidyverse)
library(ggdist)
library(ggside)
library(easystats)
library(patchwork)

illusion1 <- read.csv("../data/raw_illusion1.csv") |>
  mutate(
    Illusion_Effect = fct_relevel(as.factor(Illusion_Effect), "Incongruent", "Congruent"),
    Block = as.factor(Block)
  )

illusion2 <- read.csv("../data/raw_illusion2.csv") |>
  mutate(
    Illusion_Effect = fct_relevel(as.factor(Illusion_Effect), "Incongruent", "Congruent"),
    Block = as.factor(Block)
  )

perceptual <- read.csv("../data/raw_perceptual.csv") |>
  mutate(
    Block = as.factor(Block)
  )

sub <- read.csv("../data/raw_questionnaires.csv") |> 
  mutate(
    Education = fct_relevel(Education, "Prefer not to say", "Other", "High school", "Bachelor", "Master", "Doctorate")
  )

# For prolific:
# bayestestR::point_estimate(sub$Duration_Session1)
# plot(bayestestR::estimate_density(sub$Duration_Session1))

Outlier Detection (Tasks)

# Dear participant, thank you for participating in our study. Unfortunately, our system detected multiple issues in your data (such as implausibly short responses - in particular in the 2nd part of the study, random-like pattern of answers, or the same response to different scales - as some were designed to trigger various answers), which makes it unusable. We understand that you might have been in a hurry or had some other issues, and so we kindly ask you to return your participation; we hope to open-up more slots in the future would you be interested to participate again. 

# Dear participant, thank you for participating in our study. Unfortunately, our system detected multiple issues in your data (such as implausibly short responses - in particular in the 2nd part of the study, random-like pattern of answers, or the same response to different scales - as some were designed to trigger various answers), which makes it unusable for us. We understand that you might have been in a hurry or had some other issues; we hope to open-up more slots in the future would you be interested to participate again. 

outliers_perceptual <- c(
  "S003",
  "S008"
)
outliers_perceptual_block2 <- c(
  "S226",
  "S350"
)
outliers_illusion1 <- c(
  "S008",
  "S278",
  "S389"
  )
outliers_illusion1_block2 <- c(
  "S153",
  "S226",
  "S350"
  )
outliers_illusion2 <- c(
  "S003"
)

We removed 3, 2, and 1 participants for the illusion task - session 1, perceptual task, and illusion task - session 2 respectively, upon inspection of the average error rage (when close to 50%, suggesting random answers) and/or when the reaction time distribution was implausibly fast.

Descriptive Table

data <- rbind(illusion1, illusion2, perceptual) |>
  filter(RT < 10) |>
  mutate(
    Participant = fct_rev(Participant),
    Task = fct_relevel(Task, "Illusion_Session1", "Perceptual", "Illusion_Session2")
  )

table <- data |>
  group_by(Participant, Task) |>
  summarize(
    Error = sum(Error) / n(),
    RT = mean(RT)
  ) |>
  ungroup() |>
  arrange(desc(Error)) |>
  tidyr::pivot_wider(names_from = "Task", values_from = c("Error", "RT"), names_vary = "slowest") |>
  datawizard::data_relocate(ends_with("Session2"), after = -1) |>
  datawizard::data_relocate(ends_with("Session1"), after = 1) |>
  arrange(desc(Error_Illusion_Session1))

data.frame(Participant = c("Average"), t(sapply(table[2:ncol(table)], mean, na.rm = TRUE))) |>
  rbind(table) |>
  knitr::kable() |>
  kableExtra::row_spec(1, italic = TRUE, background = "grey", color = "white") |>
  kableExtra::row_spec(which(table$Participant %in% c(outliers_perceptual, outliers_illusion1, outliers_illusion2)) + 1, background = "#EF9A9A") |>
  kableExtra::row_spec(which(table$Participant %in% c(outliers_illusion1_block2, outliers_perceptual_block2)) + 1, background = "orange") |>
  # kableExtra::column_spec(2, color="white",
  #                         background = kableExtra::spec_color(c(NA, table$Error_Illusion_Session1))) |>
  kableExtra::kable_styling(full_width = TRUE) |>
  kableExtra::scroll_box(width = "100%", height = "500px")

Participant	Error_Illusion_Session1	RT_Illusion_Session1	Error_Perceptual	RT_Perceptual	RT_Illusion_Session2	Error_Illusion_Session2
Average	0.188	0.768	0.066	0.671	0.731	0.265
S389	0.487	0.185	0.156	0.647
S008	0.417	0.610	0.500	0.347
S110	0.391	1.519	0.323	2.553
S278	0.391	0.349	0.844	0.494
S124	0.383	0.708	0.167	0.606
S319	0.372	0.787	0.042	0.656
S153	0.370	0.575	0.109	0.699
S198	0.357	0.755	0.312	0.683
S226	0.354	0.365	0.266	0.366
S002	0.346	0.713	0.115	0.872	0.945	0.396
S023	0.346	0.631	0.125	0.619
S408	0.341	0.597	0.146	0.594
S362	0.339	0.764	0.083	0.751
S232	0.336	1.223	0.219	0.802
S299	0.323	0.712	0.214	0.584
S437	0.318	1.213	0.068	0.936
S070	0.314	1.118	0.149	1.014
S422	0.312	0.511	0.203	0.480
S117	0.305	0.490	0.182	0.412
S307	0.297	0.573	0.146	0.681
S146	0.297	0.619	0.042	0.709
S151	0.292	0.570	0.177	0.542
S328	0.289	0.543	0.130	0.611
S144	0.289	0.737	0.146	0.691
S080	0.286	0.477	0.120	0.532
S479	0.284	0.459	0.047	0.523
S266	0.284	0.601	0.104	0.717
S132	0.284	0.469	0.135	0.446
S178	0.281	0.542	0.146	0.507
S350	0.280	0.733	0.351	0.314
S246	0.279	0.445	0.073	0.412
S135	0.279	0.516	0.125	0.504
S087	0.279	0.576	0.151	0.589
S359	0.276	0.669	0.078	0.598
S341	0.271	0.563	0.042	0.585
S152	0.266	0.947	0.078	0.549
S290	0.266	0.602	0.104	0.564
S224	0.263	0.683	0.214	0.494
S174	0.263	0.617	0.062	0.730
S167	0.263	0.665	0.193	0.591
S021	0.263	0.544	0.250	0.703
S384	0.260	0.707	0.120	0.647
S333	0.260	0.831	0.052	0.883
S059	0.260	0.542	0.021	0.488
S475	0.258	0.590	0.094	0.531
S348	0.258	0.658	0.109	0.575
S251	0.258	0.632	0.052	1.205
S073	0.258	0.665	0.104	0.596
S006	0.258	0.529	0.089	0.620	0.723	0.216
S195	0.255	0.637	0.068	0.564
S154	0.254	0.615	0.141	0.528
S334	0.253	0.932	0.052	0.838
S305	0.253	0.613	0.188	0.574
S301	0.253	0.711	0.036	0.580
S173	0.253	0.754	0.062	0.760
S140	0.253	0.591	0.068	0.636
S136	0.253	0.549	0.078	0.528
S123	0.253	0.815	0.083	0.665
S367	0.250	0.551	0.099	0.584
S270	0.250	0.798	0.026	0.646
S166	0.250	0.520	0.120	0.472
S129	0.250	0.674	0.062	0.572
S094	0.250	0.602	0.089	0.514
S337	0.247	0.760	0.151	0.537
S162	0.247	0.509	0.016	0.595
S133	0.247	0.493	0.099	0.583
S112	0.247	0.490	0.073	0.492
S419	0.245	0.606	0.115	0.592
S306	0.245	0.557	0.141	0.419
S229	0.245	0.759	0.036	0.642
S053	0.245	0.511	0.151	0.475
S281	0.242	0.544	0.109	0.465
S048	0.242	0.502	0.052	0.502
S330	0.240	0.603	0.078	0.462
S203	0.240	0.825	0.047	0.633
S101	0.240	0.427	0.177	0.406
S347	0.237	0.643	0.083	0.543
S329	0.237	1.084	0.036	0.918
S316	0.237	0.543	0.104	0.594
S156	0.237	0.665	0.089	0.524
S025	0.237	0.713	0.073	0.598
S279	0.234	0.597	0.099	0.554
S211	0.234	0.561	0.057	0.590
S007	0.234	0.894	0.089	0.770
S177	0.233	0.701	0.130	0.795
S484	0.232	0.541	0.073	0.498
S373	0.232	0.729	0.047	0.763
S259	0.232	0.715	0.135	0.613
S247	0.232	0.497	0.021	0.473
S233	0.232	0.517	0.062	0.530
S217	0.232	0.558	0.089	0.482
S199	0.232	0.591	0.120	0.566
S163	0.232	0.658	0.047	0.738
S036	0.232	0.845	0.068	0.749
S402	0.229	0.785	0.036	0.813
S287	0.229	0.661	0.099	0.481
S083	0.229	0.588	0.042	0.561
S063	0.228	0.885	0.042	0.797
S324	0.227	0.739	0.047	0.637
S014	0.227	0.641	0.047	0.548
S276	0.224	0.535	0.047	0.538
S248	0.224	0.483	0.083	0.478
S244	0.224	0.575	0.172	0.476
S235	0.224	0.524	0.057	0.491
S103	0.224	0.613	0.036	0.562
S097	0.224	0.791	0.068	0.528
S019	0.224	0.618	0.052	0.496
S311	0.221	0.450	0.234	0.401
S497	0.221	0.819	0.052	0.789
S472	0.221	0.857	0.089	0.747
S320	0.221	0.565	0.104	0.690
S190	0.221	0.724	0.021	0.674
S046	0.221	0.620	0.073	0.553
S042	0.221	0.560	0.161	0.493
S289	0.220	0.883	0.089	0.566
S390	0.219	0.805	0.036	0.810
S139	0.219	0.605	0.052	0.537
S109	0.219	0.736	0.135	0.641
S092	0.217	1.202	0.036	0.810
S466	0.216	0.582	0.047	0.570
S332	0.216	0.727	0.083	0.631
S331	0.216	0.542	0.089	0.477
S295	0.216	0.949	0.021	0.582
S294	0.216	0.625	0.130	0.689
S157	0.216	0.571	0.057	0.521
S079	0.216	0.586	0.052	0.588
S207	0.214	0.669	0.083	0.578
S200	0.214	0.575	0.094	0.523
S131	0.214	0.572	0.089	0.584
S102	0.214	0.514	0.120	0.526
S250	0.213	0.761	0.147	0.803
S003	0.211	0.853	0.214	0.441	0.331	0.371
S488	0.211	1.118	0.036	0.878
S458	0.211	0.626	0.047	0.548
S452	0.211	0.546	0.031	0.600
S448	0.211	0.543	0.115	0.556
S206	0.211	0.792	0.083	0.722
S188	0.211	0.865	0.047	1.043
S107	0.211	0.808	0.036	0.722
S064	0.211	0.885	0.073	0.714
S303	0.209	0.655	0.031	0.596
S454	0.208	0.749	0.047	0.591
S453	0.208	0.714	0.125	0.570
S417	0.208	0.626	0.036	0.641
S371	0.208	0.593	0.057	0.496
S356	0.208	0.634	0.115	0.584
S298	0.208	0.551	0.083	0.527
S128	0.208	0.596	0.115	0.603
S093	0.208	0.516	0.057	0.512
S043	0.208	0.688	0.057	0.823
S214	0.206	0.679	0.042	0.591
S481	0.206	0.559	0.026	0.562
S469	0.206	0.799	0.094	0.565
S377	0.206	0.721	0.083	0.542
S366	0.206	0.656	0.021	0.675
S336	0.206	0.691	0.104	0.560
S312	0.206	0.993	0.073	0.619
S265	0.206	0.972	0.057	0.806
S175	0.206	1.272	0.109	1.099
S145	0.206	0.541	0.099	0.498
S086	0.206	0.726	0.099	0.717
S283	0.204	1.663	0.177	0.682
S405	0.203	0.915	0.052	0.846
S385	0.203	0.750	0.047	0.774
S304	0.203	0.749	0.120	0.534
S191	0.203	0.745	0.062	0.591
S116	0.203	0.760	0.104	0.635
S113	0.203	0.758	0.073	0.643
S108	0.203	0.715	0.089	0.569
S096	0.203	0.554	0.094	0.473
S499	0.201	0.595	0.156	0.501
S490	0.201	0.812	0.052	0.824
S407	0.201	0.954	0.042	0.737
S272	0.201	0.578	0.073	0.501
S242	0.201	0.986	0.010	0.748
S218	0.201	0.593	0.104	0.448
S172	0.201	0.567	0.057	0.470
S105	0.201	0.617	0.052	0.525
S100	0.201	0.740	0.083	0.730
S066	0.201	0.859	0.031	0.728
S001	0.199	0.986	0.323	0.946
S483	0.198	0.657	0.047	0.675
S409	0.198	0.630	0.115	0.578
S396	0.198	0.744	0.083	0.666
S239	0.198	0.626	0.089	0.545
S477	0.195	0.553	0.083	0.571
S456	0.195	0.654	0.099	0.569
S424	0.195	0.811	0.042	0.741
S375	0.195	0.635	0.083	0.573
S342	0.195	0.634	0.057	0.714
S227	0.195	0.734	0.047	0.670
S130	0.195	0.660	0.021	0.606
S125	0.195	0.605	0.068	0.563
S052	0.195	0.537	0.031	0.541
S495	0.193	0.761	0.042	0.713
S346	0.193	0.582	0.078	0.502
S335	0.193	0.627	0.078	0.620
S260	0.193	0.671	0.042	0.560
S122	0.193	0.621	0.089	0.556
S085	0.193	0.824	0.177	0.637
S047	0.191	0.823	0.094	0.624
S478	0.190	0.519	0.083	0.473
S425	0.190	0.762	0.057	0.698
S418	0.190	0.857	0.016	0.827
S323	0.190	0.698	0.068	0.649
S285	0.190	1.028	0.026	0.769
S237	0.190	0.859	0.031	0.733
S223	0.190	0.563	0.057	0.517
S192	0.190	0.803	0.031	0.781
S072	0.190	0.925	0.057	0.960
S496	0.188	0.754	0.083	0.713
S485	0.188	0.897	0.052	0.788
S411	0.188	0.966	0.005	0.685
S388	0.188	0.639	0.057	0.587
S277	0.188	0.636	0.078	0.532
S082	0.188	0.470	0.125	0.410
S067	0.188	0.560	0.099	0.550
S494	0.185	0.584	0.021	0.552
S441	0.185	0.700	0.036	0.585
S383	0.185	1.085	0.062	0.976
S358	0.185	0.689	0.047	0.754
S345	0.185	0.608	0.057	0.604
S321	0.185	0.831	0.062	0.687
S300	0.185	0.673	0.021	0.677
S296	0.185	0.565	0.068	0.476
S282	0.185	0.505	0.078	0.460
S267	0.185	0.530	0.042	0.418
S149	0.185	0.638	0.062	0.595
S126	0.185	0.743	0.062	0.498
S120	0.185	0.816	0.115	0.656
S115	0.185	0.703	0.089	0.480
S111	0.185	1.007	0.057	0.798
S430	0.183	1.033	0.109	1.032
S444	0.182	0.926	0.333	0.836
S487	0.182	0.625	0.068	0.559
S486	0.182	0.780	0.036	0.609
S398	0.182	0.663	0.078	0.656
S370	0.182	0.745	0.026	0.739
S253	0.182	0.701	0.026	0.609
S252	0.182	0.775	0.109	0.618
S249	0.182	0.768	0.036	0.693
S193	0.182	0.625	0.073	0.523
S186	0.182	0.706	0.104	0.588
S150	0.182	1.545	0.031	1.134
S137	0.182	0.722	0.042	0.524
S104	0.182	0.656	0.073	0.522
S026	0.182	0.934	0.036	0.732
S017	0.180	0.606	0.068	0.534
S467	0.180	1.071	0.078	0.735
S459	0.180	0.751	0.047	0.609
S449	0.180	0.829	0.099	0.682
S344	0.180	0.699	0.026	0.807
S263	0.180	0.671	0.089	0.554
S254	0.180	0.862	0.052	0.708
S225	0.180	0.803	0.057	0.587
S197	0.180	0.765	0.005	0.743
S121	0.180	0.508	0.052	0.480
S040	0.180	0.929	0.026	0.829
S089	0.178	0.888	0.031	0.603
S414	0.177	1.065	0.042	0.880
S386	0.177	0.781	0.047	0.623
S189	0.177	1.288	0.042	0.724
S044	0.177	0.665	0.016	0.642
S035	0.177	0.523	0.099	0.497
S030	0.177	0.718	0.068	0.546
S013	0.177	0.706	0.062	0.563
S470	0.174	0.644	0.042	0.605
S443	0.174	0.516	0.047	0.653
S399	0.174	0.733	0.042	0.692
S353	0.174	0.544	0.083	0.451
S349	0.174	0.631	0.021	0.963
S310	0.174	0.692	0.021	0.607
S286	0.174	0.708	0.047	0.652
S269	0.174	0.642	0.047	0.559
S228	0.174	0.572	0.036	0.485
S222	0.174	0.765	0.078	0.627
S161	0.174	0.626	0.115	0.562
S076	0.174	0.655	0.031	0.671
S034	0.174	0.792	0.099	0.645
S022	0.174	0.601	0.078	0.500
S474	0.172	1.003	0.073	0.865
S435	0.172	0.757	0.010	0.663
S434	0.172	0.895	0.031	0.861
S410	0.172	0.762	0.068	0.586
S374	0.172	1.247	0.078	0.603
S360	0.172	0.770	0.021	0.570
S351	0.172	0.797	0.036	0.768
S338	0.172	0.859	0.010	0.731
S326	0.172	0.614	0.026	0.537
S280	0.172	0.676	0.062	0.498
S262	0.172	0.587	0.109	0.529
S230	0.172	0.952	0.047	1.729
S216	0.172	0.681	0.089	0.687
S183	0.172	1.014	0.016	1.340
S158	0.172	0.631	0.073	0.575
S065	0.172	0.811	0.021	0.605
S062	0.172	0.708	0.042	0.641
S314	0.169	0.651	0.021	0.560
S209	0.169	0.564	0.079	0.509
S476	0.167	0.612	0.057	0.514
S468	0.167	0.829	0.021	0.643
S450	0.167	0.733	0.047	0.530
S445	0.167	0.452	0.104	0.405
S442	0.167	0.829	0.005	0.638
S397	0.167	0.633	0.125	0.613
S309	0.167	0.940	0.062	0.815
S264	0.167	0.902	0.036	0.675
S245	0.167	0.697	0.057	0.579
S220	0.167	0.763	0.010	0.766
S205	0.167	1.010	0.005	0.740
S181	0.167	0.746	0.062	0.736
S143	0.167	0.972	0.036	0.770
S038	0.167	0.691	0.115	0.618
S033	0.167	0.752	0.083	0.698
S024	0.167	0.735	0.042	0.756
S020	0.167	0.820	0.073	0.833
S480	0.164	0.861	0.016	0.662
S465	0.164	0.876	0.057	0.896
S447	0.164	0.840	0.005	0.689
S439	0.164	0.652	0.062	0.554
S292	0.164	0.790	0.068	0.672
S284	0.164	0.922	0.021	0.731
S258	0.164	0.756	0.068	0.514
S221	0.164	0.765	0.062	0.652
S210	0.164	0.978	0.005	0.645
S050	0.164	1.025	0.016	0.714
S009	0.164	0.833	0.010	0.633
S438	0.163	1.790	0.016	1.229
S455	0.161	1.022	0.005	0.944
S429	0.161	1.266	0.031	0.905
S421	0.161	0.718	0.052	0.672
S361	0.161	0.757	0.016	0.556
S352	0.161	0.657	0.042	0.576
S313	0.161	0.711	0.036	0.602
S201	0.161	1.008	0.036	0.712
S196	0.161	0.788	0.016	0.545
S054	0.161	0.576	0.057	0.535
S039	0.161	0.524	0.083	0.517
S004	0.161	1.051	0.010	0.800
S127	0.160	1.396	0.021	1.066
S011	0.159	0.755	0.042	0.657	0.687	0.185
S489	0.159	0.692	0.026	0.576
S413	0.159	0.909	0.057	0.689
S380	0.159	0.610	0.083	0.628
S376	0.159	0.683	0.099	0.465
S372	0.159	0.685	0.026	0.556
S363	0.159	1.236	0.099	0.918
S308	0.159	0.605	0.016	0.536
S302	0.159	0.995	0.021	0.696
S212	0.159	0.702	0.042	0.663
S194	0.159	0.755	0.073	0.666
S071	0.159	0.748	0.016	0.836
S187	0.157	1.300	0.073	0.828
S395	0.156	0.612	0.036	0.530
S268	0.156	0.646	0.047	0.630
S255	0.156	0.647	0.042	0.574
S215	0.156	0.657	0.047	0.538
S114	0.156	0.571	0.042	0.528
S068	0.156	1.011	0.052	0.624
S291	0.154	1.003	0.026	0.837
S275	0.154	0.565	0.036	0.546
S234	0.154	0.954	0.026	0.664
S032	0.154	0.550	0.031	0.585
S420	0.151	1.205	0.146	1.147
S473	0.151	0.837	0.104	0.621
S423	0.151	0.961	0.036	0.577
S403	0.151	1.077	0.052	0.502
S379	0.151	0.554	0.073	0.494
S315	0.151	0.728	0.047	1.003
S119	0.149	1.968	0.021	1.564
S498	0.148	0.715	0.042	0.587
S482	0.148	0.772	0.031	0.500
S436	0.148	0.660	0.036	0.550
S391	0.148	0.810	0.031	0.639
S261	0.148	0.714	0.031	0.674
S165	0.148	0.908	0.021	0.679
S155	0.148	0.688	0.042	0.838
S147	0.148	0.946	0.016	0.682
S088	0.148	1.056	0.026	0.878
S077	0.148	0.884	0.057	1.019
S493	0.146	0.733	0.026	0.550
S462	0.146	0.901	0.042	0.780
S440	0.146	1.028	0.036	0.817
S369	0.146	0.680	0.036	0.536
S256	0.146	0.716	0.021	0.594
S240	0.146	0.768	0.042	0.536
S236	0.146	0.861	0.000	0.635
S213	0.146	0.653	0.036	0.549
S074	0.146	0.730	0.052	0.533
S058	0.146	0.609	0.036	0.596
S057	0.146	0.645	0.021	0.562
S491	0.143	0.593	0.068	0.525
S355	0.143	0.737	0.026	0.698
S339	0.143	0.859	0.068	0.831
S288	0.143	0.881	0.016	0.691
S084	0.143	0.932	0.000	0.966
S471	0.141	0.844	0.057	0.799
S404	0.141	1.462	0.010	1.049
S343	0.141	0.761	0.010	0.686
S325	0.141	1.068	0.016	0.859
S317	0.141	0.692	0.026	0.620
S273	0.141	0.699	0.094	0.677
S202	0.141	0.641	0.062	0.513
S164	0.141	0.512	0.010	0.629
S142	0.141	0.518	0.083	0.485
S045	0.141	0.730	0.010	0.912
S392	0.138	0.738	0.042	0.727
S387	0.138	0.679	0.036	0.637
S368	0.138	0.854	0.047	0.707
S274	0.138	0.731	0.036	0.738
S179	0.138	0.738	0.026	0.725
S168	0.138	0.631	0.078	0.646
S160	0.138	0.640	0.057	0.526
S138	0.138	0.888	0.031	0.629
S340	0.136	1.142	0.047	1.066
S428	0.135	0.736	0.068	0.569
S381	0.135	0.794	0.021	0.679
S118	0.135	1.150	0.005	0.974
S015	0.135	0.580	0.047	0.643
S098	0.134	0.993	0.021	0.849
S464	0.133	0.690	0.073	0.582
S461	0.133	0.692	0.042	0.569
S394	0.133	0.642	0.021	0.590
S219	0.133	0.907	0.016	0.718
S148	0.133	0.764	0.062	0.778
S095	0.133	1.531	0.021	0.931
S500	0.130	1.020	0.016	0.753
S460	0.130	0.647	0.036	0.583
S427	0.130	0.672	0.036	0.601
S243	0.130	0.705	0.000	0.676
S208	0.130	1.116	0.026	0.804
S185	0.130	0.802	0.005	0.579
S180	0.130	0.742	0.031	0.616
S171	0.130	1.159	0.036	0.856
S091	0.130	0.673	0.031	0.561
S081	0.130	0.733	0.021	0.718
S075	0.130	1.089	0.068	0.890
S060	0.130	0.947	0.042	0.695
S041	0.130	0.751	0.052	0.672
S446	0.128	0.838	0.010	0.838
S365	0.128	0.828	0.000	0.658
S357	0.128	0.837	0.000	0.636
S318	0.128	1.066	0.000	0.955
S231	0.128	0.784	0.016	0.644
S051	0.128	0.753	0.016	0.569
S037	0.128	0.965	0.047	0.756
S018	0.128	0.816	0.052	0.682
S016	0.128	0.678	0.021	0.605
S061	0.126	1.281	0.021	0.593
S463	0.125	0.841	0.026	0.659
S431	0.125	0.664	0.036	0.772
S416	0.125	1.056	0.026	1.011
S141	0.125	0.657	0.062	0.572
S055	0.125	0.756	0.057	0.553
S031	0.125	0.780	0.016	0.669
S005	0.125	0.877	0.000	0.999
S182	0.123	1.166	0.031	0.846
S010	0.122	1.152	0.068	1.439	0.968	0.159
S415	0.122	1.296	0.021	0.780
S271	0.122	1.322	0.026	0.993
S238	0.122	0.965	0.031	0.738
S099	0.122	0.691	0.016	0.696
S027	0.122	0.730	0.010	0.706
S426	0.120	0.930	0.005	0.711
S393	0.120	0.681	0.031	0.537
S378	0.120	1.135	0.016	0.781
S134	0.120	0.688	0.021	0.635
S433	0.117	1.244	0.016	0.732
S354	0.117	0.920	0.016	0.648
S204	0.117	0.719	0.026	0.623
S169	0.117	1.828	0.036	1.431
S028	0.117	0.887	0.052	0.775
S241	0.115	0.740	0.109	0.587
S176	0.115	1.080	0.016	0.606
S106	0.115	0.581	0.016	0.543
S056	0.115	0.664	0.052	0.568
S432	0.112	1.023	0.005	0.869
S364	0.112	0.829	0.068	0.607
S184	0.111	1.733	0.016	1.934
S457	0.109	0.834	0.047	0.694
S382	0.109	0.938	0.052	0.920
S297	0.109	0.788	0.036	0.593
S159	0.109	0.738	0.036	0.724
S401	0.107	1.062	0.010	0.683
S069	0.107	0.893	0.010	0.859
S400	0.104	0.915	0.031	0.811
S257	0.104	1.620	0.016	1.348
S078	0.104	1.021	0.000	1.016
S492	0.102	0.754	0.010	0.698
S412	0.099	0.782	0.026	0.672
S406	0.096	0.748	0.010	0.537
S322	0.096	0.690	0.016	0.599
S293	0.096	0.965	0.031	1.032
S090	0.096	0.809	0.026	0.610
S049	0.096	0.968	0.042	0.990
S170	0.094	0.970	0.032	0.891
S451	0.094	0.884	0.021	0.816
S029	0.094	0.924	0.068	0.875
S012	0.094	0.928	0.016	0.699
S327	0.086	0.933	0.005	0.690

Reaction Time Distribution

plot_distribution <- function(data) {
  data |>
    estimate_density(select = "RT", at = c("Participant", "Task", "Block")) |>
    group_by(Participant) |>
    normalize(select = "y") |>
    ungroup() |>
    mutate(
      # Participant = fct_relevel(Participant, as.character(table$Participant)),
      color = case_when(
        Participant %in% outliers_perceptual & Task == "Perceptual" ~ "red",
        Participant %in% outliers_illusion1 & Task == "Illusion_Session1" ~ "red",
        Participant %in% outliers_illusion2 & Task == "Illusion_Session2" ~ "red",
        Participant %in% outliers_perceptual_block2 & Task == "Perceptual" ~ "orange",
        Participant %in% outliers_illusion1_block2 & Task == "Illusion_Session1" ~ "orange",
        TRUE ~ "blue"
      ),
      Task = fct_recode(Task,
        "Illusion task (session 1)" = "Illusion_Session1",
        # "Illusion task (session 2)" = "Illusion_Session2",
        "Perceptual task" = "Perceptual"
      )
    ) |>
    ggplot(aes(x = x, y = y)) +
    geom_area(data = normalize(estimate_density(data, select = "RT"), select = "y"), alpha = 0.2) +
    geom_line(aes(color = color, group = interaction(Participant, Block), linetype = Block), size = 0.5) +
    # geom_vline(xintercept = 0.125, linetype = "dashed", color = "red", size = 0.5) +
    scale_color_manual(values = c("red" = "#F44336", "orange" = "#FF9800", "blue" = "blue"), guide = "none") +
    scale_x_continuous(expand = c(0, 0)) +
    scale_y_continuous(expand = c(0, 0)) +
    coord_cartesian(xlim = c(0, 2)) +
    theme_modern() +
    theme(axis.text.y = element_blank(),
          axis.line.y = element_blank(),
          strip.text.y = element_text(size = rel(0.6))) +
    facet_grid(Participant ~ Task) +
    labs(y = "", x = "Reaction Time (s)")
}

p <- list()
for(i in 1:5) {
  p[[i]] <- data |>
  filter((as.numeric(gsub("\\D", "", Participant)) > (i - 1) * 100) & (as.numeric(gsub("\\D", "", Participant)) <= 100 * i)) |>
  plot_distribution()
}
p <- patchwork::wrap_plots(p, ncol=5, nrow=1) + plot_layout(guides = "collect")
ggsave("figures/1_Preprocessing-outliers_RT.png", p, width = 7*5, height = 24, dpi = 150)

knitr::include_graphics("figures/1_Preprocessing-outliers_RT.png")

illusion1 <- filter(illusion1, !Participant %in% outliers_illusion1)
illusion1 <- filter(illusion1, !(Participant %in% outliers_illusion1_block2 & Block == 2))
illusion2 <- filter(illusion2, !Participant %in% outliers_illusion2)
perceptual <- filter(perceptual, !Participant %in% outliers_perceptual)
perceptual <- filter(perceptual, !(Participant %in% outliers_perceptual_block2 & Block == 2))

Outliers Detection (Blocks)

For each block, we computed the error rate and, if more than 50%, we discarded the whole block (as it likely indicates that instructions got mixed up, for instance participants were selecting the smaller instead of the bigger circle).

data <- rbind(illusion1, illusion2, perceptual) |>
  group_by(Participant, Task, Illusion_Type, Block) |>
  summarize(ErrorRate_per_block = sum(Error) / n()) |>
  ungroup() |>
  arrange(desc(ErrorRate_per_block))


data |>
  estimate_density(at = c("Task", "Illusion_Type", "Block"), method = "KernSmooth") |>
  ggplot(aes(x = x, y = y)) +
  geom_line(aes(color = Illusion_Type, linetype = Block)) +
  geom_vline(xintercept = 0.5, linetype = "dashed") +
  scale_x_continuous(expand = c(0, 0)) +
  scale_y_continuous(expand = c(0, 0)) +
  scale_color_manual(values = c("Ebbinghaus" = "#2196F3", "MullerLyer" = "#4CAF50", "VerticalHorizontal" = "#FF5722")) +
  labs(y = "Distribution", x = "Error Rate") +
  theme_modern() +
  facet_wrap(~Task)

remove_badblocks <- function(df) {
  n <- nrow(df)
  df <- df |>
    group_by(Participant, Illusion_Type, Block) |>
    mutate(ErrorRate_per_block = sum(Error) / n()) |>
    ungroup() |>
    filter(ErrorRate_per_block < 0.5) |>
    select(-ErrorRate_per_block)
  
  text <- paste0(
    "We removed ",
    n - nrow(df),
    " (",
    insight::format_value((n - nrow(df)) / n, as_percent = TRUE),
    ") trials belonging to bad blocks."
  )
  list(data = df, text = text)
}

out <- remove_badblocks(illusion1)
print(paste("Illusion (session 1):", out$text))

[1] “Illusion (session 1): We removed 704 (0.37%) trials belonging to bad blocks.”

illusion1 <- out$data

out <- remove_badblocks(illusion2)
print(paste("Illusion (session 2):", out$text))

[1] “Illusion (session 2): We removed 64 (4.17%) trials belonging to bad blocks.”

illusion2 <- out$data

out <- remove_badblocks(perceptual)
print(paste("Perceptual task:", out$text))

[1] “Perceptual task: We removed 544 (0.57%) trials belonging to bad blocks.”

perceptual <- out$data

Outliers Detection (Trials)

Reaction Time per Trial

check_trials <- function(df) {
  data <- df |>
    mutate(Outlier = ifelse(RT >= 10, TRUE, FALSE)) |>
    group_by(Participant) |>
    mutate(Outlier = ifelse(RT < 0.125 | standardize(RT, robust = TRUE) > 4, TRUE, Outlier)) |>
    ungroup()

  p1 <- data |>
    filter(RT < 10) |>
    estimate_density(select = "RT", at = "Participant") |>
    group_by(Participant) |>
    normalize(select = "y") |>
    ungroup() |>
    merge(data |>
      group_by(Participant) |>
      mutate(Threshold = median(RT) + 4 * mad(RT)) |>
      filter(Error == 0) |>
      summarize(Threshold = mean(Threshold))) |>
    mutate(Outlier = ifelse(x >= Threshold, TRUE, FALSE)) |>
    ggplot(aes(x = x, y = y)) +
    geom_area(data = normalize(estimate_density(filter(data, RT < 10), select = "RT"), select = "y"), alpha = 0.2) +
    geom_line(aes(color = Participant, linetype = Outlier), alpha = 0.2) +
    geom_vline(xintercept = c(125), linetype = "dashed", color = "red") +
    scale_color_material_d("rainbow", guide = "none") +
    scale_x_continuous(expand = c(0, 0)) +
    scale_y_continuous(expand = c(0, 0)) +
    guides(linetype = "none") +
    coord_cartesian(xlim = c(0, 5)) +
    theme_modern() +
    theme(axis.text.y = element_blank()) +
    labs(y = "", x = "Reaction Time (s)")


  p2 <- data |>
    group_by(Participant) |>
    summarize(Outlier = sum(Outlier) / nrow(illusion1)) |>
    mutate(Participant = fct_reorder(Participant, Outlier)) |>
    ggplot(aes(x = Participant, y = Outlier)) +
    geom_bar(stat = "identity", aes(fill = Participant)) +
    scale_fill_material_d("rainbow", guide = "none") +
    scale_x_discrete(expand = c(0, 0)) +
    scale_y_continuous(expand = c(0, 0), labels = scales::percent) +
    see::theme_modern() +
    theme(axis.text.x = element_blank()) +
    labs(y = "Percentage of outlier trials")

  text <- paste0(
    "We removed ",
    sum(data$Outlier),
    " (",
    insight::format_value(sum(data$Outlier) / nrow(data), as_percent = TRUE),
    ") outlier trials (125 ms < RT < 4 MAD above median)."
  )

  data <- filter(data, Outlier == FALSE)
  data$Outlier <- NULL

  list(p = p1 / p2, data = data, text = text)
}

Illusion Task (Session 1)

out <- check_trials(illusion1)
print(paste("Illusion (session 1):", out$text))

[1] “Illusion (session 1): We removed 6735 (3.55%) outlier trials (125 ms < RT < 4 MAD above median).”

out$p

illusion1 <- out$data

Illusion Task (Session 2)

out <- check_trials(illusion2)
print(paste("Illusion (session 2):", out$text))

[1] “Illusion (session 2): We removed 49 (3.33%) outlier trials (125 ms < RT < 4 MAD above median).”

out$p

illusion2 <- out$data

Perceptual Task

out <- check_trials(perceptual)
print(paste("Perceptual task:", out$text))

[1] “Perceptual task: We removed 4664 (4.92%) outlier trials (125 ms < RT < 4 MAD above median).”

out$p

perceptual <- out$data

Outlier Detection (Questionnaires)

Multivariate Detection

We compute a multivariate outlier score.

outliers <- sub |> 
  select(AttentionCheck_Session1, 
         IPIP6_RT, PID5_RT, GCBS_RT, ASQ_RT, LIE_RT, SPQ_RT, 
         IPIP6_SD, PID5_SD, GCBS_SD, ASQ_SD, LIE_SD, SPQ_SD, 
         PHQ4_SD) |> 
  standardize() |> 
  performance::check_outliers(method = c("mahalanobis", "mahalanobis_robust", "mcd", "ics"))

sub$Outlier_Questionnaire <- as.data.frame(outliers)$Outlier
# outliers

Manual Check

# < 0.80 to the average attention check and 1 in outlier score
outliers_questionnaires <- c(
  "S003", "S008", "S047", "S068", "S110", "S127", "S151", "S189", "S261", "S266", "S390", "S489", "S494"
)

We removed the questionnaire data from 13 participants upon inspection of attention checks and time taken to complete each questionnaires.

table <- sub |>
  mutate(
    Outlier_Task1 = Participant %in% outliers_illusion1,
    Outlier_Task1b = Participant %in% outliers_illusion1_block2 / 2,
    Outlier_Task2 = Participant %in% outliers_illusion2,
    Outlier_Task3 = Participant %in% outliers_perceptual,
    Outlier_Task3b = Participant %in% outliers_perceptual_block2 / 2,
    Outlier_Tasks = Outlier_Task1 + Outlier_Task1b + 
      Outlier_Task2 + 
      Outlier_Task3 + Outlier_Task3b
  ) |>
  select(
    Participant,
    Outlier_Tasks,
    Outlier_Questionnaire,
    AttentionCheck_Session1,
    IPIP6_RT, PID5_RT, ASQ_RT, SPQ_RT,
    IPIP6_SD, PID5_SD, PHQ4_SD,
    AttentionCheck_Session2,
    BPD_RT, MAIA_RT, PI_RT,
    BPD_SD, MAIA_SD, PI_SD
  ) |> 
  # mutate(across(ends_with("IPIP6_RT") | ends_with("IPIP6_SD"), standardize)) |> 
  # arrange(desc(Outlier_Tasks), AttentionCheck_Session1) 
  arrange(desc(Participant))

t <- data.frame(Participant = c("Average"), t(sapply(table[2:ncol(table)], mean, na.rm = TRUE))) |>
  rbind(table) |>
  knitr::kable() |>
  kableExtra::row_spec(1, italic = TRUE) |>
  kableExtra::row_spec(which(table$Participant %in% outliers_questionnaires) + 1, background = "#EF9A9A")

for (i in 2:ncol(table)) {
  t <- kableExtra::column_spec(
    t, i,
    color = "white",
    background = kableExtra::spec_color(
      c(NA, table[[i]]),
      option = "D",
      alpha = 1,
      # direction = ifelse(str_detect(names(table)[i], "_SD|Outlier"), 1, -1),
      na_color = "white",
    )
  )
}


t  |>
  kableExtra::row_spec(1, background = "grey") |> 
  kableExtra::kable_styling(full_width = TRUE, font_size = 9) |>
  kableExtra::scroll_box(width = "100%", height = "500px")

Participant	Outlier_Tasks	Outlier_Questionnaire	AttentionCheck_Session1	IPIP6_RT	PID5_RT	ASQ_RT	SPQ_RT	IPIP6_SD	PID5_SD	PHQ4_SD	AttentionCheck_Session2	BPD_RT	MAIA_RT	PI_RT	BPD_SD	MAIA_SD	PI_SD
Average	0.017	0.149	0.966	1.757	2.518	2.644	3.086	0.191	0.679	0.397	0.656	1.052	2.99	3.55	0.241	0.129	0.701
S500	0.000	0.000	1.000	2.152	2.515	2.119	3.357	0.080	0.589	0.354
S499	0.000	0.000	1.000	1.358	1.247	1.449	2.843	0.141	0.597	0.000
S498	0.000	0.000	1.000	1.410	2.037	2.403	3.236	0.261	0.780	0.354
S497	0.000	0.500	1.000	1.334	4.179	1.574	2.262	0.274	0.974	0.707
S496	0.000	0.000	1.000	2.285	1.544	1.588	1.692	0.240	0.769	0.707
S495	0.000	0.000	0.939	1.070	1.668	1.902	2.171	0.175	0.817	0.354
S494	0.000	0.500	0.668	1.350	0.996	1.223	1.337	0.211	0.508	0.000
S493	0.000	0.000	1.000	0.855	1.174	1.286	1.566	0.136	0.713	0.000
S492	0.000	0.000	1.000	1.815	1.971	2.290	2.577	0.166	0.597	0.000
S491	0.000	0.000	1.000	1.547	1.894	3.160	3.661	0.178	0.309	0.354
S490	0.000	0.000	1.000	1.008	1.660	1.690	1.944	0.168	0.933	0.000
S489	0.000	0.500	0.772	1.425	1.728	1.942	2.380	0.296	0.597	1.061
S488	0.000	0.000	1.000	3.671	3.699	3.928	5.844	0.114	0.268	0.000
S487	0.000	0.500	0.799	1.148	1.954	2.538	2.899	0.150	0.288	0.354
S486	0.000	0.000	1.000	1.289	2.222	2.475	2.942	0.206	0.753	0.354
S485	0.000	0.000	1.000	0.985	1.331	1.218	1.556	0.148	0.793	0.000
S484	0.000	0.000	1.000	1.103	1.128	1.778	1.908	0.147	0.219	0.000
S483	0.000	0.000	1.000	1.078	1.528	2.180	2.185	0.096	0.559	0.000
S482	0.000	0.000	0.893	2.017	2.087	2.301	2.726	0.175	0.825	0.000
S481	0.000	0.000	1.000	1.491	1.903	1.921	2.422	0.221	0.623	0.354
S480	0.000	0.500	0.994	1.217	2.055	1.730	2.726	0.145	0.820	0.354
S479	0.000	0.000	1.000	2.022	2.098	2.393	3.819	0.109	0.450	0.354
S478	0.000	0.000	1.000	1.020	1.765	2.004	2.980	0.081	0.528	0.000
S477	0.000	0.000	1.000	1.345	2.031	3.069	2.267	0.177	0.288	0.000
S476	0.000	0.000	1.000	1.173	1.378	1.441	1.822	0.216	0.854	0.707
S475	0.000	0.000	1.000	3.121	2.987	3.611	3.808	0.248	0.358	0.354
S474	0.000	0.000	1.000	2.046	3.418	2.702	4.368	0.102	0.597	0.354
S473	0.000	0.000	0.964	1.721	2.013	2.245	3.805	0.189	0.636	0.354
S472	0.000	0.000	0.996	1.055	1.887	1.906	2.766	0.253	0.892	0.707
S471	0.000	0.000	1.000	1.194	2.236	2.027	3.571	0.128	0.733	1.061
S470	0.000	1.000	0.906	1.657	2.900	36.735	3.249	0.192	0.765	0.000
S469	0.000	0.500	0.929	1.936	4.377	2.366	4.967	0.194	0.939	0.000
S468	0.000	0.000	1.000	1.721	2.148	2.389	3.304	0.106	0.802	0.000
S467	0.000	0.500	0.981	3.028	5.796	5.871	6.819	0.067	0.577	0.354
S466	0.000	0.000	0.929	0.992	1.659	1.935	2.350	0.117	0.999	0.707
S465	0.000	0.500	1.000	2.655	6.778	2.986	3.717	0.121	0.686	0.354
S464	0.000	0.000	1.000	1.346	1.734	1.858	2.873	0.164	0.822	0.354
S463	0.000	0.500	1.000	1.144	2.580	4.053	3.803	0.170	0.736	0.707
S462	0.000	0.500	1.000	2.981	3.195	3.622	5.789	0.181	0.597	0.000
S461	0.000	0.000	0.996	1.627	1.803	1.882	2.838	0.224	0.675	0.000
S460	0.000	0.000	1.000	0.973	1.492	2.015	2.327	0.170	0.880	0.707
S459	0.000	0.500	0.857	2.207	4.385	3.471	4.551	0.372	0.750	0.707
S458	0.000	0.000	1.000	1.413	1.572	1.795	2.028	0.212	0.366	0.000
S457	0.000	0.000	0.964	1.023	1.508	1.613	1.913	0.292	0.598	0.354
S456	0.000	0.000	1.000	1.802	2.127	2.273	3.147	0.183	0.539	0.354
S455	0.000	0.000	1.000	1.523	2.928	3.872	3.580	0.323	0.589	0.000
S454	0.000	0.000	1.000	1.151	1.839	1.537	1.972	0.182	0.704	0.000
S453	0.000	0.000	1.000	0.649	1.024	1.211	1.384	0.137	0.358	0.000
S452	0.000	0.000	1.000	0.916	2.441	1.401	1.721	0.096	0.386	0.707
S451	0.000	0.000	0.999	1.394	1.544	1.628	2.044	0.153	0.199	0.000
S450	0.000	0.000	1.000	1.055	1.365	1.887	2.397	0.178	0.398	0.000
S449	0.000	0.500	0.964	1.876	5.459	2.893	5.794	0.373	0.467	0.000
S448	0.000	0.000	0.857	1.176	2.117	2.249	1.827	0.186	0.398	0.354
S447	0.000	0.000	1.000	1.985	1.919	2.338	2.526	0.157	0.635	0.000
S446	0.000	0.750	0.929	2.662	9.281	9.664	5.270	0.181	0.591	0.000
S445	0.000	0.000	0.993	1.170	1.639	1.490	2.015	0.138	0.701	0.000
S444	0.000	0.000	0.964	0.832	0.937	2.017	2.812	0.233	0.509	0.000
S443	0.000	0.000	1.000	1.646	1.581	2.470	2.658	0.270	0.508	0.000
S442	0.000	0.000	1.000	1.367	1.844	2.285	2.524	0.205	0.288	0.000
S441	0.000	0.000	1.000	0.908	1.274	1.271	1.951	0.215	0.609	0.707
S440	0.000	0.500	0.847	3.895	4.232	4.473	4.230	0.170	0.646	0.354
S439	0.000	0.000	0.909	1.037	1.485	1.395	3.111	0.187	0.816	0.707
S438	0.000	0.000	0.909	2.666	3.005	3.875	3.239	0.112	0.398	0.000
S437	0.000	0.000	0.964	2.567	3.659	3.170	4.034	0.112	0.791	0.000
S436	0.000	0.000	1.000	2.059	2.682	2.929	4.007	0.155	0.656	0.707
S435	0.000	0.500	1.000	5.149	1.818	2.264	3.842	0.195	0.597	0.000
S434	0.000	0.000	1.000	1.417	1.668	1.900	2.097	0.207	0.268	0.000
S433	0.000	0.000	1.000	1.977	2.041	3.603	2.873	0.164	0.089	1.061
S432	0.000	0.500	1.000	5.170	6.957	5.273	6.912	0.176	0.548	0.707
S431	0.000	0.000	0.929	2.082	3.009	2.810	4.377	0.232	0.701	0.000
S430	0.000	0.000	1.000	2.275	1.550	2.438	2.225	0.154	0.594	0.707
S429	0.000	0.000	0.929	1.773	2.629	2.549	3.425	0.111	0.597	0.354
S428	0.000	0.000	1.000	1.353	1.715	2.391	2.245	0.225	0.756	0.354
S427	0.000	0.000	0.964	0.988	1.179	1.343	1.797	0.198	0.802	0.354
S426	0.000	0.000	1.000	2.800	3.298	2.952	4.105	0.160	0.770	0.707
S425	0.000	0.000	0.964	1.218	1.852	1.799	2.402	0.247	0.822	0.707
S424	0.000	0.000	1.000	1.035	1.345	1.719	1.955	0.136	0.470	0.000
S423	0.000	0.000	1.000	1.996	2.617	2.397	3.507	0.232	0.976	0.354
S422	0.000	0.500	1.000	0.930	1.088	3.206	1.474	0.204	0.744	0.000
S421	0.000	0.000	1.000	1.921	2.370	2.797	2.852	0.210	0.637	0.000
S420	0.000	0.250	1.000	1.693	3.918	2.396	2.771	0.180	0.900	0.354
S419	0.000	0.000	0.927	2.243	2.959	3.137	4.554	0.175	0.747	0.707
S418	0.000	0.000	0.929	2.518	2.519	3.710	4.558	0.336	0.591	0.707
S417	0.000	0.500	0.893	1.544	3.196	3.891	3.337	0.261	0.577	0.354
S416	0.000	0.000	0.929	1.998	2.787	3.576	3.767	0.244	0.488	0.354
S415	0.000	0.000	1.000	2.190	2.475	2.966	3.830	0.173	0.704	0.000
S414	0.000	0.500	1.000	3.295	6.307	3.120	4.905	0.210	0.862	0.000
S413	0.000	0.000	1.000	2.029	2.585	2.423	4.052	0.073	0.565	0.354
S412	0.000	0.000	0.964	0.988	1.339	1.798	2.039	0.144	0.881	1.061
S411	0.000	0.500	0.857	1.541	2.198	2.846	5.589	0.353	0.977	0.707
S410	0.000	0.500	0.860	1.377	3.288	3.352	4.919	0.202	0.790	0.354
S409	0.000	0.000	1.000	1.403	1.948	2.047	2.448	0.282	0.436	0.000
S408	0.000	0.500	0.964	1.233	2.487	2.292	4.261	0.103	0.424	0.707
S407	0.000	0.000	0.821	0.754	1.716	1.718	1.973	0.178	0.796	0.354
S406	0.000	0.000	1.000	0.764	1.010	1.244	1.949	0.099	0.539	0.354
S405	0.000	0.000	1.000	1.243	1.461	2.238	2.399	0.093	0.179	0.354
S404	0.000	0.000	1.000	1.753	2.605	2.569	2.319	0.202	0.864	0.000
S403	0.000	0.000	0.929	0.835	1.029	1.006	1.488	0.158	0.577	0.354
S402	0.000	0.000	0.964	1.112	1.384	1.688	1.892	0.198	0.650	0.354
S401	0.000	0.000	1.000	1.543	2.280	2.172	2.323	0.130	0.578	0.354
S400	0.000	0.000	0.964	2.461	3.903	3.167	4.653	0.196	0.618	0.000
S399	0.000	0.000	1.000	2.039	4.241	2.835	3.381	0.217	0.643	0.354
S398	0.000	0.000	0.964	0.987	1.159	1.480	1.519	0.201	0.793	0.354
S397	0.000	0.500	1.000	2.362	2.901	2.980	3.754	0.220	0.779	0.000
S396	0.000	0.000	1.000	1.049	1.383	1.547	1.869	0.141	0.589	0.354
S395	0.000	0.000	1.000	0.995	1.213	1.526	1.579	0.256	0.790	0.354
S394	0.000	0.000	0.964	1.983	2.782	3.075	3.496	0.149	0.684	1.414
S393	0.000	0.500	1.000	3.238	3.484	3.482	3.599	0.274	1.128	0.354
S392	0.000	0.000	1.000	0.880	1.104	1.464	1.815	0.108	0.358	0.000
S391	0.000	1.000	0.883	1.963	2.519	16.085	5.164	0.215	0.557	0.000
S390	0.000	0.500	0.797	1.068	1.744	2.132	1.173	0.036	0.000	0.000
S389	1.000	0.000	0.883	0.976	1.244	1.499	0.891	0.209	0.745	1.061
S388	0.000	0.000	1.000	1.006	1.015	1.373	1.528	0.246	0.946	0.354
S387	0.000	0.000	0.881	1.398	2.335	2.165	2.453	0.276	0.894	0.000
S386	0.000	0.000	0.809	1.403	2.314	2.364	2.474	0.136	0.615	0.354
S385	0.000	0.000	0.883	2.021	1.864	2.012	2.422	0.182	0.655	0.354
S384	0.000	1.000	1.000	4.145	7.418	9.643	6.283	0.155	0.656	0.354
S383	0.000	0.000	0.857	2.025	2.833	3.001	3.498	0.296	0.905	0.354
S382	0.000	0.000	1.000	1.322	1.865	2.084	2.254	0.208	0.675	0.354
S381	0.000	0.000	1.000	1.146	1.984	2.006	2.622	0.141	0.765	0.354
S380	0.000	0.000	0.957	1.471	1.633	1.946	2.817	0.146	0.629	0.000
S379	0.000	0.000	1.000	2.965	2.272	3.183	3.625	0.232	0.985	0.707
S378	0.000	0.000	1.000	2.425	4.388	3.619	5.145	0.117	0.815	0.707
S377	0.000	0.500	1.000	2.427	3.722	5.139	5.178	0.264	0.487	0.000
S376	0.000	0.000	0.999	1.006	1.669	1.764	2.052	0.193	0.843	0.707
S375	0.000	0.000	1.000	1.140	1.401	1.622	2.051	0.210	0.508	0.354
S374	0.000	0.000	0.964	0.833	1.678	2.215	2.446	0.147	0.585	0.707
S373	0.000	0.000	1.000	2.300	2.868	4.121	4.823	0.235	0.537	1.061
S372	0.000	0.000	1.000	1.204	1.542	1.681	1.919	0.208	0.597	0.707
S371	0.000	0.000	1.000	1.009	1.448	1.591	1.989	0.097	0.450	0.354
S370	0.000	0.500	1.000	1.112	2.344	3.959	2.988	0.157	0.736	0.354
S369	0.000	0.500	1.000	3.974	2.381	3.692	2.903	0.273	1.059	0.354
S368	0.000	1.000	0.964	3.890	5.642	3.103	7.225	0.201	0.669	0.354
S367	0.000	0.000	0.817	1.543	1.853	2.402	2.799	0.086	0.545	0.000
S366	0.000	0.500	0.800	0.945	2.117	0.863	2.667	0.159	0.649	0.707
S365	0.000	0.250	0.914	2.834	2.259	2.029	3.803	0.167	0.918	1.061
S364	0.000	0.000	1.000	1.367	2.460	2.138	2.805	0.163	0.876	1.414
S363	0.000	0.000	1.000	1.316	1.810	2.432	3.296	0.314	0.687	0.707
S362	0.000	0.000	1.000	1.043	1.944	2.111	2.449	0.220	0.814	0.707
S361	0.000	0.500	0.929	1.597	2.361	2.018	2.899	0.218	0.710	0.000
S360	0.000	0.000	1.000	1.003	1.322	1.522	1.716	0.208	1.339	0.000
S359	0.000	0.000	1.000	1.102	2.096	2.132	2.835	0.116	0.626	0.354
S358	0.000	0.250	1.000	2.137	1.879	2.210	3.424	0.184	0.110	0.707
S357	0.000	0.000	1.000	1.873	1.757	1.450	2.224	0.122	0.736	0.354
S356	0.000	0.500	0.964	1.638	8.675	2.701	3.368	0.161	0.984	0.000
S355	0.000	1.000	0.857	7.354	16.200	6.168	5.644	0.217	1.067	0.354
S354	0.000	0.000	1.000	1.877	1.896	1.915	2.729	0.177	0.832	0.000
S353	0.000	0.000	1.000	1.102	1.872	1.743	2.106	0.189	0.704	0.707
S352	0.000	0.000	1.000	1.802	2.610	2.557	3.432	0.148	0.915	0.000
S351	0.000	0.000	1.000	1.842	1.479	1.659	2.113	0.233	0.736	0.354
S350	1.000	0.500	0.809	2.331	0.834	1.098	1.506	0.149	0.528	0.354
S349	0.000	0.000	1.000	2.419	2.293	2.330	2.801	0.102	0.398	0.000
S348	0.000	0.000	1.000	2.404	3.883	3.435	4.724	0.195	1.026	1.061
S347	0.000	0.000	0.909	1.811	2.162	2.394	3.429	0.322	0.794	0.707
S346	0.000	0.000	0.917	0.979	1.242	1.324	1.589	0.292	1.061	0.354
S345	0.000	0.500	1.000	1.751	3.694	3.467	2.877	0.191	0.618	0.354
S344	0.000	0.000	1.000	1.572	3.368	2.547	3.644	0.244	0.822	1.414
S343	0.000	0.000	1.000	2.303	2.798	3.598	3.459	0.222	0.786	0.707
S342	0.000	0.000	1.000	1.699	2.692	2.310	3.125	0.262	0.793	0.000
S341	0.000	0.750	1.000	2.313	4.555	4.486	3.517	0.359	1.429	0.000
S340	0.000	0.500	0.929	1.787	1.880	3.759	4.951	0.218	0.963	0.354
S339	0.000	0.000	1.000	1.064	2.105	1.743	2.153	0.158	0.843	0.707
S338	0.000	0.000	0.993	1.384	1.528	1.529	2.685	0.126	0.875	0.707
S337	0.000	0.000	1.000	1.037	1.266	1.436	1.760	0.228	0.725	0.354
S336	0.000	0.000	1.000	1.476	2.025	2.363	3.170	0.170	0.822	0.000
S335	0.000	0.000	1.000	0.712	1.284	1.842	2.818	0.110	0.358	0.354
S334	0.000	0.500	0.964	1.208	2.237	3.518	1.825	0.152	0.580	0.000
S333	0.000	0.000	1.000	1.202	1.185	1.561	1.624	0.109	0.843	0.354
S332	0.000	0.000	1.000	1.316	1.989	1.853	2.264	0.160	0.752	0.000
S331	0.000	0.500	1.000	1.112	3.467	2.818	2.065	0.202	0.854	0.707
S330	0.000	0.500	1.000	1.441	1.544	4.800	3.562	0.177	0.655	0.354
S329	0.000	0.000	1.000	2.855	2.610	3.528	4.327	0.150	0.666	0.707
S328	0.000	0.500	1.000	3.013	1.552	4.204	3.203	0.201	0.927	0.354
S327	0.000	0.000	1.000	2.116	3.950	3.017	3.482	0.178	1.020	0.000
S326	0.000	0.000	1.000	0.999	1.225	1.239	1.643	0.150	0.789	0.354
S325	0.000	0.500	1.000	1.329	1.863	1.876	2.395	0.204	0.487	0.000
S324	0.000	0.000	0.929	3.091	2.698	3.277	3.702	0.232	0.725	0.707
S323	0.000	0.000	1.000	0.954	1.318	1.337	1.440	0.139	0.398	0.354
S322	0.000	0.500	0.964	1.727	1.920	11.400	2.623	0.131	0.816	0.000
S321	0.000	0.000	1.000	1.994	2.965	3.001	3.601	0.174	0.508	0.000
S320	0.000	0.000	1.000	1.026	1.391	1.414	1.812	0.295	0.440	0.354
S319	0.000	0.000	1.000	1.316	1.822	1.462	2.878	0.186	0.869	0.000
S318	0.000	0.500	1.000	2.888	3.035	4.544	6.508	0.157	0.537	0.354
S317	0.000	0.000	1.000	0.957	1.183	1.579	1.584	0.132	0.509	0.707
S316	0.000	0.000	0.929	2.119	2.942	2.736	3.698	0.124	0.545	1.414
S315	0.000	0.000	0.964	2.642	2.798	2.771	3.306	0.110	0.705	0.354
S314	0.000	0.000	1.000	1.222	1.737	1.842	2.104	0.200	1.103	0.000
S313	0.000	0.000	0.964	1.260	1.770	1.902	2.423	0.168	0.718	1.768
S312	0.000	0.500	1.000	2.630	2.567	3.040	3.058	0.285	0.805	0.000
S311	0.000	0.000	0.964	2.117	2.602	2.534	4.364	0.167	0.701	0.354
S310	0.000	0.000	0.994	1.220	1.609	1.737	2.171	0.160	0.782	0.000
S309	0.000	0.000	1.000	1.624	2.438	3.253	3.039	0.230	0.733	0.354
S308	0.000	0.000	1.000	1.766	2.443	2.317	3.115	0.166	0.476	0.707
S307	0.000	0.000	1.000	1.573	2.674	2.665	4.045	0.209	0.901	0.707
S306	0.000	0.000	1.000	0.997	2.128	1.622	2.302	0.158	1.001	0.000
S305	0.000	0.000	0.821	2.060	2.704	3.046	3.275	0.250	0.858	0.354
S304	0.000	0.250	0.964	1.562	2.407	2.427	4.065	0.151	0.539	1.414
S303	0.000	1.000	0.857	1.155	15.210	5.229	2.523	0.199	0.776	0.707
S302	0.000	0.000	1.000	1.380	2.716	2.630	2.567	0.232	0.597	0.354
S301	0.000	0.000	1.000	1.924	2.567	2.683	3.260	0.175	0.943	0.707
S300	0.000	0.500	1.000	2.687	4.192	4.659	6.309	0.253	0.794	0.707
S299	0.000	0.500	0.929	1.506	2.880	1.561	1.693	0.212	0.372	0.000
S298	0.000	0.000	1.000	1.472	1.670	1.649	2.160	0.185	0.179	0.354
S297	0.000	0.000	1.000	1.394	1.852	1.771	2.433	0.177	0.456	0.000
S296	0.000	0.000	1.000	1.717	2.151	2.343	2.976	0.246	0.566	0.000
S295	0.000	0.500	0.857	2.627	2.803	2.288	2.554	0.160	0.655	0.707
S294	0.000	0.000	1.000	1.067	2.716	2.439	2.611	0.156	0.571	0.000
S293	0.000	0.000	1.000	1.049	1.290	1.278	1.958	0.162	0.410	0.354
S292	0.000	0.000	1.000	2.112	2.665	2.828	3.951	0.146	0.545	0.707
S291	0.000	0.500	1.000	2.883	2.509	2.919	3.700	0.230	1.029	0.354
S290	0.000	0.000	1.000	1.095	1.399	1.992	1.185	0.184	0.456	0.000
S289	0.000	1.000	1.000	1.556	2.332	2.902	4.347	0.124	0.577	0.707
S288	0.000	0.000	1.000	2.379	2.603	3.321	5.287	0.148	0.378	0.000
S287	0.000	0.000	1.000	0.868	1.080	1.163	1.450	0.162	0.802	0.354
S286	0.000	0.000	0.929	2.812	3.347	3.457	4.707	0.267	0.776	0.707
S285	0.000	0.000	1.000	0.985	1.235	1.394	1.855	0.134	0.487	0.000
S284	0.000	0.000	1.000	1.857	3.196	3.195	2.708	0.178	0.904	0.354
S283	0.000	0.500	1.000	1.316	4.915	2.641	4.322	0.374	0.974	1.414
S282	0.000	0.500	1.000	1.189	1.717	3.888	2.281	0.291	0.858	0.000
S281	0.000	0.000	0.964	1.695	2.629	1.810	2.928	0.107	0.450	0.000
S280	0.000	0.000	0.964	1.159	1.737	1.541	2.072	0.167	0.456	0.707
S279	0.000	0.000	0.964	2.911	2.591	2.780	3.600	0.191	0.788	0.000
S278	1.000	0.000	1.000	1.555	1.575	1.718	2.001	0.173	0.647	0.000
S277	0.000	1.000	0.893	1.290	2.730	2.494	12.004	0.063	0.392	0.000
S276	0.000	0.000	0.993	2.842	3.699	3.919	5.737	0.178	0.655	0.707
S275	0.000	0.000	1.000	2.478	3.357	4.457	4.614	0.282	0.219	0.000
S274	0.000	0.000	1.000	1.477	1.331	1.437	2.077	0.334	0.430	0.000
S273	0.000	0.500	0.964	1.992	8.126	2.835	6.016	0.159	0.788	0.354
S272	0.000	0.000	0.929	1.298	1.878	1.832	2.807	0.179	0.539	0.354
S271	0.000	0.000	0.845	1.778	2.592	3.001	3.467	0.213	0.825	0.354
S270	0.000	0.000	0.964	1.611	2.360	2.212	4.238	0.165	0.765	1.061
S269	0.000	0.500	1.000	3.522	6.198	3.841	5.593	0.137	0.983	0.707
S268	0.000	0.000	1.000	1.497	1.886	1.778	2.513	0.095	0.539	0.354
S267	0.000	0.000	1.000	1.392	1.699	1.945	2.302	0.135	0.540	0.707
S266	0.000	1.000	0.611	1.110	2.100	1.638	2.123	0.349	0.830	0.000
S265	0.000	0.000	0.964	1.500	1.872	1.898	2.526	0.202	0.816	0.000
S264	0.000	0.000	1.000	2.461	2.640	2.763	4.513	0.205	0.537	0.354
S263	0.000	0.000	1.000	1.402	1.735	2.508	4.953	0.208	0.777	0.707
S262	0.000	0.000	0.964	1.466	2.022	2.298	2.404	0.127	0.487	0.354
S261	0.000	0.500	0.761	1.692	3.659	4.919	4.466	0.144	0.717	0.354
S260	0.000	0.000	1.000	1.430	1.443	2.151	2.007	0.176	0.430	0.354
S259	0.000	0.000	1.000	1.390	1.403	1.628	2.106	0.169	0.808	0.000
S258	0.000	0.000	1.000	1.418	1.765	2.149	2.599	0.139	0.932	0.354
S257	0.000	0.000	1.000	2.908	3.005	2.264	3.581	0.216	1.002	0.354
S256	0.000	0.000	1.000	1.433	1.780	1.952	2.504	0.263	0.923	0.707
S255	0.000	0.000	0.964	0.914	1.177	1.103	1.920	0.237	0.688	0.000
S254	0.000	0.500	1.000	3.150	3.900	5.346	5.268	0.190	0.984	0.354
S253	0.000	0.000	1.000	1.886	2.400	2.671	2.995	0.093	0.309	0.354
S252	0.000	0.000	1.000	1.082	1.366	1.485	1.847	0.211	0.329	1.414
S251	0.000	1.000	0.842	2.490	9.121	10.209	8.107	0.217	0.566	0.707
S250	0.000	0.250	0.831	1.630	0.996	1.070	1.461	0.212	0.559	0.707
S249	0.000	0.000	1.000	2.662	3.282	2.877	3.917	0.256	0.309	0.354
S248	0.000	0.000	1.000	0.857	1.349	1.258	1.734	0.173	0.687	0.707
S247	0.000	0.000	1.000	0.914	1.203	1.397	1.897	0.150	0.534	0.707
S246	0.000	0.000	0.964	1.585	1.886	2.916	2.855	0.161	0.597	0.354
S245	0.000	0.000	0.999	1.112	1.376	1.830	1.806	0.173	0.467	0.354
S244	0.000	0.000	1.000	0.953	1.281	1.560	1.686	0.131	0.728	0.000
S243	0.000	1.000	1.000	7.331	5.069	4.736	5.369	0.143	0.528	0.000
S242	0.000	0.000	1.000	1.201	1.539	1.483	2.115	0.264	0.802	1.061
S241	0.000	0.000	0.893	1.175	2.083	1.585	1.329	0.122	0.467	0.354
S240	0.000	0.500	1.000	2.894	3.176	3.971	4.478	0.142	0.705	1.061
S239	0.000	0.000	1.000	2.289	2.245	2.572	2.499	0.210	0.650	0.000
S238	0.000	0.000	1.000	2.070	2.288	2.816	3.668	0.296	0.676	0.000
S237	0.000	0.000	1.000	1.361	2.993	1.490	2.610	0.137	0.955	0.354
S236	0.000	0.000	0.960	0.934	1.143	1.283	1.829	0.240	0.519	0.000
S235	0.000	0.000	1.000	2.383	2.271	2.403	2.334	0.172	0.838	0.354
S234	0.000	0.000	1.000	1.212	1.691	1.982	2.604	0.210	0.849	0.000
S233	0.000	0.000	0.929	1.401	2.989	3.622	2.917	0.089	0.784	0.000
S232	0.000	0.000	1.000	1.761	3.785	3.646	3.405	0.205	0.525	0.000
S231	0.000	0.000	1.000	1.645	2.005	2.036	2.196	0.200	0.926	0.707
S230	0.000	0.000	1.000	1.914	1.967	2.041	2.239	0.153	0.418	0.000
S229	0.000	0.000	1.000	1.723	1.708	2.732	2.950	0.131	0.779	0.354
S228	0.000	0.000	1.000	1.488	1.607	1.963	2.861	0.193	0.863	0.354
S227	0.000	0.000	0.964	1.066	1.827	1.870	1.657	0.187	0.629	0.707
S226	1.000	0.250	1.000	3.319	2.895	3.100	3.128	0.160	0.643	1.061
S225	0.000	0.000	1.000	1.641	3.665	2.710	2.831	0.128	0.612	0.000
S224	0.000	1.000	0.997	1.217	4.576	1.838	2.326	0.154	0.565	0.354
S223	0.000	0.500	0.929	1.219	1.775	3.688	2.220	0.356	0.934	1.061
S222	0.000	0.500	0.979	1.162	5.108	1.766	1.887	0.198	0.719	0.354
S221	0.000	0.000	1.000	1.763	3.545	2.856	3.950	0.152	0.834	0.354
S220	0.000	0.000	1.000	1.259	1.672	1.834	3.072	0.261	0.558	0.354
S219	0.000	0.000	1.000	2.332	2.565	2.827	3.985	0.157	0.661	0.000
S218	0.000	0.000	1.000	1.692	2.157	1.918	3.558	0.313	0.646	0.000
S217	0.000	0.000	0.832	1.126	2.446	1.516	2.970	0.129	0.655	0.707
S216	0.000	0.000	0.863	1.110	1.271	1.821	1.819	0.139	0.519	0.707
S215	0.000	0.000	0.964	1.078	2.644	2.500	3.646	0.177	0.585	1.414
S214	0.000	0.000	1.000	2.363	1.928	2.262	3.313	0.188	0.724	0.354
S213	0.000	0.000	1.000	1.363	1.957	1.964	2.115	0.188	0.487	0.000
S212	0.000	0.000	1.000	1.946	2.575	2.921	3.251	0.288	0.825	1.061
S211	0.000	0.000	1.000	1.293	1.909	1.711	3.389	0.201	0.626	0.354
S210	0.000	0.500	1.000	1.487	5.489	1.694	2.440	0.142	0.643	0.707
S209	0.000	0.000	1.000	1.174	1.598	1.537	1.818	0.144	0.407	0.707
S208	0.000	0.000	1.000	1.826	2.777	1.934	3.004	0.181	0.967	0.707
S207	0.000	0.000	0.964	0.923	2.363	1.500	2.005	0.115	0.713	0.354
S206	0.000	0.000	1.000	2.218	2.882	2.923	3.004	0.154	0.549	0.354
S205	0.000	0.000	1.000	1.691	3.114	2.646	2.991	0.096	0.741	0.707
S204	0.000	0.000	1.000	1.502	2.257	2.018	2.572	0.204	1.073	0.707
S203	0.000	0.500	0.900	2.347	1.547	4.431	4.086	0.128	0.693	0.354
S202	0.000	0.000	1.000	1.514	1.530	3.165	2.867	0.114	0.000	0.000
S201	0.000	0.000	1.000	1.520	2.244	2.145	2.828	0.240	0.779	0.000
S200	0.000	0.000	0.893	1.161	2.862	2.185	1.961	0.205	0.863	0.000
S199	0.000	0.500	0.857	1.475	1.957	2.210	2.558	0.245	0.737	0.354
S198	0.000	0.500	1.000	3.866	1.979	1.958	2.454	0.269	0.537	0.354
S197	0.000	0.000	1.000	2.106	2.034	2.028	3.471	0.315	0.615	0.354
S196	0.000	0.000	1.000	1.047	2.106	1.463	1.922	0.204	0.528	0.707
S195	0.000	0.000	1.000	1.344	1.335	1.407	1.988	0.130	0.199	0.000
S194	0.000	0.000	1.000	1.344	1.777	2.121	3.638	0.295	0.525	0.354
S193	0.000	0.000	1.000	1.170	1.814	1.873	2.174	0.168	0.724	0.707
S192	0.000	0.000	1.000	1.372	1.715	1.964	2.305	0.183	0.802	0.707
S191	0.000	0.000	1.000	1.085	1.395	1.595	3.164	0.145	0.704	1.061
S190	0.000	0.000	0.913	1.328	1.929	2.072	2.971	0.169	0.525	0.707
S189	0.000	1.000	0.595	1.268	4.890	1.909	2.418	0.229	0.828	0.000
S188	0.000	0.000	0.929	2.201	2.724	2.608	4.604	0.202	0.668	0.354
S187	0.000	0.250	0.917	2.538	4.190	3.347	4.068	0.406	0.973	0.354
S186	0.000	0.500	1.000	2.081	2.853	2.921	3.352	0.136	0.916	0.354
S185	0.000	0.000	1.000	0.853	1.105	1.626	1.819	0.170	0.657	0.707
S184	0.000	0.500	0.843	2.114	5.858	7.475	5.366	0.242	0.617	0.354
S183	0.000	0.000	1.000	1.898	3.311	2.808	4.702	0.211	0.814	0.000
S182	0.000	0.000	1.000	2.719	3.090	3.467	4.974	0.156	0.834	0.707
S181	0.000	0.250	0.964	1.938	3.761	3.473	4.387	0.224	0.797	0.000
S180	0.000	0.000	0.950	1.185	2.342	1.426	2.299	0.064	0.462	0.354
S179	0.000	0.250	1.000	2.990	2.102	2.797	4.539	0.154	0.358	0.707
S178	0.000	0.000	1.000	1.321	1.784	1.567	2.550	0.194	0.834	0.354
S177	0.000	0.500	0.926	1.667	3.152	5.510	3.462	0.232	0.629	0.000
S176	0.000	0.000	0.964	2.410	3.243	3.747	4.315	0.272	0.796	0.000
S175	0.000	0.500	0.893	2.497	2.310	3.097	6.320	0.202	0.739	1.061
S174	0.000	0.500	0.964	1.572	2.908	2.124	7.362	0.083	0.663	0.707
S173	0.000	0.000	1.000	1.561	2.609	2.147	3.123	0.246	0.724	0.000
S172	0.000	0.000	0.857	1.778	2.397	2.265	2.895	0.318	0.859	1.061
S171	0.000	0.000	0.929	1.335	2.256	2.601	2.723	0.149	0.487	0.354
S170	0.000	0.500	0.905	2.818	6.842	5.090	5.707	0.293	1.037	0.707
S169	0.000	0.000	1.000	2.534	2.809	3.751	5.201	0.236	0.854	0.707
S168	0.000	0.000	1.000	1.916	2.226	1.748	2.163	0.184	0.545	0.000
S167	0.000	0.000	1.000	0.813	1.325	1.300	2.202	0.249	1.127	0.707
S166	0.000	0.000	1.000	0.926	1.113	1.126	1.459	0.162	0.635	0.000
S165	0.000	0.000	1.000	1.699	2.933	2.793	3.059	0.196	0.908	0.707
S164	0.000	0.000	1.000	1.006	1.283	1.474	1.791	0.124	0.467	0.000
S163	0.000	0.500	1.000	1.618	2.576	6.214	3.047	0.122	0.719	0.354
S162	0.000	0.000	0.973	2.022	2.397	2.974	3.504	0.132	0.557	0.000
S161	0.000	0.250	1.000	2.168	3.121	3.229	5.050	0.301	0.961	0.354
S160	0.000	0.000	1.000	1.608	3.534	1.646	2.242	0.154	0.692	0.000
S159	0.000	0.000	0.964	0.970	1.526	1.697	2.031	0.144	0.687	0.000
S158	0.000	0.000	1.000	1.553	1.578	1.817	2.292	0.129	0.366	0.000
S157	0.000	0.000	1.000	1.395	2.264	2.050	3.377	0.137	0.585	0.354
S156	0.000	0.000	1.000	1.118	1.418	1.802	1.844	0.207	0.737	0.354
S155	0.000	0.250	1.000	1.599	2.294	2.304	3.285	0.329	0.671	1.768
S154	0.000	0.000	1.000	0.979	1.271	1.328	1.867	0.185	0.637	0.354
S153	0.500	0.000	0.964	1.959	1.466	1.382	2.978	0.160	1.068	1.061
S152	0.000	0.500	1.000	1.255	2.559	8.312	2.170	0.349	0.903	0.707
S151	0.000	1.000	0.787	6.055	1.806	7.617	1.062	0.199	0.655	1.414
S150	0.000	0.000	0.929	1.602	1.898	2.199	2.757	0.247	0.758	0.354
S149	0.000	0.000	1.000	1.038	1.291	1.402	1.797	0.117	0.724	0.354
S148	0.000	1.000	0.804	3.082	1.542	11.678	5.329	0.167	1.056	0.354
S147	0.000	0.000	1.000	2.631	2.598	3.734	4.462	0.093	0.644	0.354
S146	0.000	0.250	1.000	0.877	1.449	1.356	1.819	0.157	1.108	0.707
S145	0.000	0.000	1.000	1.724	2.164	2.095	3.415	0.188	0.785	0.707
S144	0.000	0.000	1.000	1.564	3.449	2.245	2.949	0.303	0.561	0.354
S143	0.000	0.000	0.964	1.230	1.597	1.831	2.758	0.176	0.638	0.000
S142	0.000	0.000	1.000	1.166	1.522	1.615	2.256	0.265	0.888	0.354
S141	0.000	0.000	0.929	1.679	3.655	2.994	3.882	0.223	0.979	1.414
S140	0.000	0.000	1.000	2.317	2.107	2.418	2.455	0.203	0.585	0.707
S139	0.000	0.000	0.857	2.020	2.878	2.427	3.706	0.252	0.823	1.061
S138	0.000	0.000	1.000	1.607	2.167	2.391	3.089	0.099	0.450	0.000
S137	0.000	0.000	1.000	2.415	3.982	3.379	4.709	0.201	0.802	0.707
S136	0.000	0.000	1.000	1.253	1.406	1.455	1.588	0.212	0.687	0.354
S135	0.000	0.000	1.000	1.269	1.598	1.561	1.911	0.147	0.626	1.061
S134	0.000	0.000	1.000	1.375	1.852	1.804	2.320	0.185	0.656	0.000
S133	0.000	0.000	1.000	1.079	1.699	1.365	1.155	0.164	0.398	0.354
S132	0.000	0.000	0.952	1.508	1.876	2.020	2.664	0.143	0.667	0.354
S131	0.000	0.000	0.964	1.548	3.060	2.143	3.262	0.174	0.765	0.707
S130	0.000	0.000	0.951	1.389	1.623	2.126	3.081	0.246	0.664	0.354
S129	0.000	0.000	1.000	2.034	1.930	2.243	3.098	0.235	0.727	0.707
S128	0.000	0.000	0.944	1.295	1.707	2.099	2.268	0.071	0.724	0.000
S127	0.000	1.000	0.750	1.872	14.156	2.988	3.551	0.260	0.768	0.354
S126	0.000	0.000	0.999	0.958	1.471	2.260	3.916	0.161	0.557	1.061
S125	0.000	0.000	1.000	0.904	1.103	0.945	1.365	0.122	0.629	0.707
S124	0.000	0.000	1.000	1.127	1.696	1.590	3.555	0.212	0.803	0.707
S123	0.000	0.000	0.964	1.012	1.659	2.681	2.070	0.189	0.467	0.707
S122	0.000	0.500	0.964	2.966	3.771	4.138	2.754	0.216	0.981	0.354
S121	0.000	0.500	1.000	1.091	2.171	3.481	2.519	0.101	0.571	0.354
S120	0.000	0.250	1.000	2.460	4.160	2.681	2.985	0.194	0.528	0.000
S119	0.000	0.500	0.964	3.599	3.987	5.267	5.465	0.122	0.447	0.000
S118	0.000	0.000	1.000	1.461	2.936	2.002	2.378	0.156	0.539	0.000
S117	0.000	0.250	0.893	2.431	1.215	1.241	2.588	0.253	0.864	0.707
S116	0.000	0.000	0.964	1.238	1.922	2.067	2.462	0.207	0.687	0.354
S115	0.000	0.000	1.000	1.634	1.648	1.923	2.453	0.135	0.728	0.000
S114	0.000	0.000	0.977	0.964	1.467	1.984	2.204	0.137	0.742	1.061
S113	0.000	0.500	1.000	2.235	2.564	4.278	3.450	0.164	0.692	0.000
S112	0.000	0.000	1.000	1.542	1.687	1.797	2.863	0.239	0.816	0.354
S111	0.000	0.000	1.000	1.346	2.048	1.928	2.283	0.225	0.908	0.000
S110	0.000	1.000	0.444	0.500	1.035	0.625	1.052	0.216	0.956	0.707
S109	0.000	0.000	0.929	1.942	2.720	2.470	3.267	0.212	0.984	0.707
S108	0.000	0.000	1.000	1.043	1.789	1.661	2.620	0.200	0.687	0.707
S107	0.000	0.250	1.000	1.123	1.424	1.703	2.584	0.277	0.814	0.707
S106	0.000	0.000	1.000	1.551	1.918	2.582	3.230	0.263	0.920	0.000
S105	0.000	0.500	1.000	1.146	1.703	3.678	2.709	0.101	0.838	0.707
S104	0.000	0.000	0.874	1.208	2.154	1.813	1.564	0.169	0.727	0.707
S103	0.000	0.000	1.000	1.111	2.064	1.916	2.653	0.077	0.557	0.000
S102	0.000	0.000	0.970	1.148	2.116	1.962	2.562	0.166	0.819	0.707
S101	0.000	0.000	1.000	1.567	1.772	2.167	2.586	0.189	0.309	0.354
S100	0.000	0.000	1.000	1.696	2.091	1.793	2.910	0.141	0.577	0.000
S099	0.000	0.750	0.886	2.410	2.758	2.462	5.870	0.391	0.724	0.000
S098	0.000	0.000	1.000	1.644	1.681	1.968	3.404	0.207	0.957	0.707
S097	0.000	0.000	1.000	1.009	1.301	1.626	1.790	0.118	0.410	0.354
S096	0.000	0.000	1.000	1.673	1.483	1.753	2.445	0.350	0.924	1.414
S095	0.000	0.000	1.000	1.345	1.592	1.836	1.822	0.150	0.774	0.707
S094	0.000	0.000	0.964	1.700	2.307	2.572	4.046	0.185	0.855	0.000
S093	0.000	0.000	1.000	1.897	2.166	2.882	3.538	0.135	0.724	0.000
S092	0.000	0.000	1.000	1.178	2.504	2.125	2.874	0.200	0.814	0.354
S091	0.000	0.000	0.893	0.852	1.412	1.357	2.734	0.090	0.707	0.707
S090	0.000	0.000	1.000	1.984	2.113	2.294	3.323	0.246	0.618	0.354
S089	0.000	1.000	0.891	6.854	2.193	2.354	2.849	0.201	0.545	0.354
S088	0.000	0.000	1.000	2.068	2.503	3.000	4.065	0.237	0.410	0.000
S087	0.000	0.250	1.000	1.566	4.313	2.873	2.848	0.196	0.652	0.707
S086	0.000	0.250	0.924	2.013	2.597	2.479	3.682	0.292	0.834	0.000
S085	0.000	0.000	0.880	1.307	3.385	2.514	2.843	0.164	0.756	0.354
S084	0.000	0.000	1.000	1.795	1.887	2.720	3.042	0.206	0.797	0.354
S083	0.000	0.500	1.000	2.247	4.753	4.815	5.163	0.214	0.110	0.354
S082	0.000	0.000	0.999	0.789	1.058	1.190	1.354	0.291	1.384	0.354
S081	0.000	0.000	0.964	1.177	2.558	2.437	2.485	0.166	0.825	0.707
S080	0.000	0.500	1.000	1.130	3.723	2.102	3.188	0.426	0.817	1.061
S079	0.000	0.500	1.000	1.320	2.051	2.116	4.948	0.253	0.836	0.000
S078	0.000	0.000	1.000	1.120	1.865	1.645	2.061	0.170	0.418	0.354
S077	0.000	0.000	1.000	1.327	1.885	1.707	2.353	0.360	0.862	0.354
S076	0.000	0.000	0.964	1.597	2.249	2.194	2.502	0.153	0.675	0.707
S075	0.000	0.000	1.000	1.848	3.184	3.326	4.551	0.218	0.858	0.354
S074	0.000	0.000	0.929	1.309	1.640	1.664	1.860	0.186	0.713	0.707
S073	0.000	0.000	0.964	1.626	1.868	1.930	2.479	0.190	0.666	0.000
S072	0.000	1.000	1.000	1.283	14.469	2.321	2.315	0.175	0.559	0.707
S071	0.000	0.000	1.000	1.652	2.506	2.479	2.670	0.185	0.834	0.354
S070	0.000	0.250	0.788	1.907	2.070	2.267	2.458	0.169	0.643	0.000
S069	0.000	0.500	0.952	3.627	1.232	1.318	6.019	0.192	0.509	0.707
S068	0.000	0.500	0.621	1.335	1.479	2.720	3.725	0.163	0.320	0.354
S067	0.000	0.000	0.910	1.005	1.141	1.345	1.457	0.186	0.545	0.707
S066	0.000	1.000	1.000	2.697	3.905	6.625	5.193	0.437	0.868	1.061
S065	0.000	0.000	0.964	1.282	1.868	2.154	2.847	0.226	0.675	0.000
S064	0.000	0.000	1.000	2.103	3.373	2.784	4.023	0.079	0.823	0.354
S063	0.000	0.000	0.891	1.521	1.713	2.049	2.047	0.188	0.676	0.354
S062	0.000	0.000	1.000	1.922	2.015	2.030	2.409	0.084	0.534	0.354
S061	0.000	0.500	1.000	0.817	6.877	1.362	1.873	0.145	0.509	0.000
S060	0.000	0.000	0.964	1.567	2.094	2.395	2.996	0.210	0.509	0.354
S059	0.000	0.000	0.997	2.304	2.234	2.914	2.421	0.255	0.907	0.707
S058	0.000	0.000	1.000	2.149	3.804	2.734	4.261	0.209	0.647	1.414
S057	0.000	0.000	1.000	3.019	2.526	2.324	3.804	0.167	0.724	0.354
S056	0.000	0.000	1.000	1.477	1.661	2.534	2.419	0.181	0.577	1.061
S055	0.000	0.000	0.964	1.084	1.428	1.200	1.911	0.237	0.715	0.000
S054	0.000	0.000	0.857	2.392	3.006	2.951	3.400	0.158	0.597	0.707
S053	0.000	0.000	1.000	1.324	2.183	1.636	2.435	0.117	0.571	0.000
S052	0.000	0.000	1.000	1.873	2.227	2.108	2.541	0.140	0.537	0.354
S051	0.000	0.000	1.000	2.072	2.736	2.599	3.642	0.157	0.199	0.354
S050	0.000	0.000	1.000	1.454	2.037	2.662	2.679	0.216	0.460	0.000
S049	0.000	0.500	0.929	2.178	4.859	3.562	5.110	0.207	0.528	0.000
S048	0.000	0.000	1.000	1.377	1.914	2.253	2.993	0.196	0.537	0.354
S047	0.000	1.000	0.779	4.321	1.188	0.905	3.752	0.184	0.089	0.000
S046	0.000	0.000	1.000	1.099	1.136	1.422	1.599	0.100	0.666	0.707
S045	0.000	0.000	0.893	2.371	2.143	2.942	3.046	0.258	0.606	0.354
S044	0.000	0.000	0.964	1.625	2.098	2.295	3.221	0.170	0.699	0.354
S043	0.000	0.000	0.964	1.304	1.868	1.949	2.288	0.219	0.398	0.354
S042	0.000	0.000	1.000	1.204	1.659	1.917	2.408	0.160	0.545	1.061
S041	0.000	0.000	1.000	1.455	1.949	1.693	2.056	0.181	0.732	0.354
S040	0.000	0.000	1.000	1.422	1.965	1.220	1.954	0.121	0.687	0.707
S039	0.000	0.000	1.000	2.092	3.134	2.945	2.904	0.190	0.656	0.707
S038	0.000	0.500	0.964	3.351	6.988	3.231	6.149	0.196	0.687	0.354
S037	0.000	0.500	1.000	0.770	4.167	2.955	1.453	0.104	0.398	0.354
S036	0.000	0.000	0.996	1.325	1.921	1.766	2.582	0.226	0.728	0.354
S035	0.000	0.000	0.993	2.358	2.258	2.601	2.810	0.182	0.837	0.354
S034	0.000	0.000	1.000	2.966	3.338	4.372	5.711	0.182	0.617	0.354
S033	0.000	0.000	1.000	0.692	0.890	1.091	1.226	0.088	0.288	0.000
S032	0.000	0.000	1.000	1.131	1.565	2.121	2.215	0.148	0.736	0.000
S031	0.000	0.000	0.964	1.509	1.611	1.729	1.971	0.224	0.830	0.354
S030	0.000	0.500	0.776	3.296	2.679	4.596	4.462	0.222	0.948	0.000
S029	0.000	0.500	0.913	1.302	6.534	3.338	3.826	0.167	1.146	0.000
S028	0.000	0.000	0.964	1.741	3.268	2.695	3.601	0.172	0.585	0.707
S027	0.000	0.000	1.000	1.369	1.777	2.340	4.058	0.161	0.675	0.000
S026	0.000	0.500	1.000	4.696	5.658	5.382	6.233	0.173	0.790	0.354
S025	0.000	0.500	1.000	2.561	2.680	5.594	4.803	0.317	0.748	0.000
S024	0.000	0.000	1.000	2.115	3.116	3.465	3.902	0.182	0.835	1.414
S023	0.000	0.000	1.000	1.548	1.875	2.191	2.886	0.277	0.674	0.000
S022	0.000	0.000	1.000	1.121	1.435	1.802	2.783	0.217	0.610	0.000
S021	0.000	1.000	1.000	4.232	3.404	6.555	7.422	0.484	0.819	1.061
S020	0.000	0.000	0.860	1.631	2.575	2.375	3.247	0.256	1.017	1.414
S019	0.000	0.000	0.893	1.980	2.789	3.059	5.708	0.205	0.744	0.354
S018	0.000	0.000	1.000	1.658	2.039	2.027	2.613	0.146	0.656	1.061
S017	0.000	0.000	0.964	1.299	1.681	1.911	2.055	0.201	0.937	0.354
S016	0.000	0.500	0.964	4.064	5.145	3.684	5.762	0.076	0.551	0.354
S015	0.000	0.000	1.000	1.045	1.275	1.418	2.595	0.292	0.713	0.354
S014	0.000	0.000	1.000	0.818	1.350	1.324	1.521	0.225	0.467	0.354
S013	0.000	0.000	1.000	1.071	1.270	1.418	2.425	0.093	0.710	0.000
S012	0.000	0.000	0.917	3.183	5.186	5.265	5.370	0.193	0.577	0.354
S011	0.000	0.500	1.000	1.871	2.802	2.380	3.382	0.155	0.814	0.354	0.667	1.188	3.28	3.53	0.313	0.130	0.769
S010	0.000	0.000	0.964	1.848	2.864	2.614	3.647	0.263	1.243	0.000	0.667	1.624	4.46	5.13	0.307	0.138	0.737
S009	0.000	0.000	1.000	1.347	2.064	2.250	2.512	0.296	0.635	0.354
S008	2.000	1.000	0.667	3.125	0.986	1.307	1.290	0.024	0.000	0.000
S007	0.000	0.000	0.929	1.095	1.324	1.792	2.001	0.211	0.702	0.707
S006	0.000	0.000	1.000	1.950	2.418	2.383	3.761	0.290	0.960	0.354	0.667	0.930	3.35	3.41	0.324	0.131	0.556
S005	0.000	0.000	1.000	1.828	2.952	2.998	3.546	0.163	0.577	0.707
S004	0.000	1.000	0.893	5.980	2.109	2.576	3.286	0.187	0.713	0.354
S003	2.000	0.000	0.952	0.955	1.375	2.160	1.962	0.216	0.847	0.000	0.613	0.719	1.59	3.71	0.102	0.098	0.819
S002	0.000	0.000	0.917	1.690	2.410	2.997	2.706	0.254	0.571	0.354	0.667	0.798	2.27	1.96	0.159	0.146	0.624
S001	0.000	0.750	0.728	1.912	2.523	4.542	7.272	0.179	0.659	0.707

# Inspection: select(sub[sub$Participant == "S199", ], starts_with("AttentionCheck"))

sub[
  sub$Participant %in% outliers_questionnaires,
  names(sub)[!names(sub) %in% c(
    "Participant", "Nationality", "Age",
    "Ethnicity", "Sex", "Student", "Education",
    "Interval", "AttentionCheck_Session1",
    "AttentionCheck_Session2"
  )]
] <- NA

Final Sample

We collected data from 500 participants.

illusion1 <- illusion1[!illusion1$Participant %in% outliers_illusion1, ]
illusion2 <- illusion2[!illusion2$Participant %in% outliers_illusion1, ]
perceptual <- perceptual[!perceptual$Participant %in% outliers_illusion1, ]
sub <- sub[!sub$Participant %in% outliers_illusion1, ]

The final sample included 497 participants (Mean age = 30.0, SD = 10.1, range: [18, 73]; Sex: 49.9% females, 50.1% males, 0.0% other; Education: Prefer not to say, 0.20%; Other, 2.41%; High school, 34.21%; Bachelor, 45.07%; Master, 16.30%; Doctorate, 1.81%), from which 2 (0.40%) completed session 2.

Country of Origin

select(sub, region = Nationality) |>
  group_by(region) |>
  summarize(n = n()) |>
  right_join(map_data("world"), by = "region") |>
  ggplot(aes(long, lat, group = group)) +
  geom_polygon(aes(fill = n)) +
  scale_fill_gradientn(colors = c("#FFEB3B", "red", "purple")) +
  labs(fill = "Number") +
  theme_void() +
  ggtitle("Number of participants by country of origin")

Age

estimate_density(sub$Age) |>
  normalize(select = y) |> 
  ggplot(aes(x = x, y = y)) +
  geom_area(fill = "#607D8B") +
  geom_vline(xintercept = mean(sub$Age), color = "red") +
  geom_label(data = data.frame(x = mean(sub$Age) * 1.1, y = 0.95), color = "red", label = paste0("Mean = ", format_value(mean(sub$Age)))) +
  scale_x_continuous(expand = c(0, 0)) +
  scale_y_continuous(expand = c(0, 0)) +
  labs(title = "Age", y = "Distribution", color = NULL) +
  theme_modern(axis.title.space = 10) +
  theme(
    plot.title = element_text(size = rel(1), face = "bold", hjust = 0.5),
    plot.subtitle = element_text(face = "italic", hjust = 0.5),
    axis.text.y = element_blank(),
    axis.text.x = element_text(size = rel(0.8)),
    axis.title.x = element_blank()
  )

Ethnicity

plot_waffle <- function(sub, what = "Nationality", title = what, rows = 8, size = 3) {
  ggwaffle::waffle_iron(sub, what, rows = rows) |>
    ggplot(aes(x, y)) +
    geom_point(aes(color = group), shape = "square", size = size) +
    coord_equal() +
    ggtitle(title) +
    labs(fill = "", color = "") +
    theme_void() +
    theme(
      plot.title = element_text(face = "bold", hjust = 0.5),
      legend.key.height = unit(1, "mm"),
      legend.key.width = unit(1, "mm")
    )
}

plot_waffle(sub, "Ethnicity", rows = 20, size = 5) +
  scale_color_manual(values = c("Hispanic" = "#FF5722", "Caucasian" = "#2196F3", "African" = "#4CAF50", "Asian" = "#FFC107", "Other" = "#795548"))

Education

sub |>
  ggplot(aes(x = Education)) +
  geom_bar(aes(fill = Education)) +
  scale_y_continuous(expand = c(0, 0), breaks= scales::pretty_breaks()) +
  scale_fill_viridis_d(guide = "none") +
  labs(title = "Education", y = "Number of Participants") +
  theme_modern(axis.title.space = 15) +
  theme(
    plot.title = element_text(size = rel(1), face = "bold", hjust = 0.5),
    plot.subtitle = element_text(face = "italic", hjust = 0.5),
    axis.text.y = element_text(size = rel(0.8)),
    axis.text.x = element_text(size = rel(0.8)),
    axis.title.x = element_blank()
  )

Save Preprocessed

write.csv(illusion1, "../data/preprocessed_illusion1.csv", row.names = FALSE)
write.csv(illusion2, "../data/preprocessed_illusion2.csv", row.names = FALSE)
write.csv(perceptual, "../data/preprocessed_perceptual.csv", row.names = FALSE)
write.csv(sub, "../data/preprocessed_questionnaires.csv", row.names = FALSE)